A lithium ion secondary battery has established its position as a high-capacity and lightweight power source indispensable for, for example, a portable electronic terminal or an electric car. An active material containing an olivine-type crystal represented by the general formula LiFePO4 has attracted attention as a positive electrode active material for the lithium ion secondary battery. It is known that when a particle diameter of such active material is reduced, a specific surface area involved in reactions for inserting and extracting lithium ions increases to activate the reactions, and hence battery characteristics improve (see, for example, Patent Literature 1).
However, lithium, which is used in the lithium ion secondary battery, poses a concern about a problem such as a worldwide increase in raw material cost. Accordingly, a sodium ion secondary battery using sodium as an alternative to lithium has been investigated in recent years. In Patent Literature 2, as a positive electrode active material, there is disclosed an active material containing an NaxMyP2O7 (where M represents at least one or more kinds of transition metal elements selected from Cr, Fe, Mn, Co, and Ni, x falls within a range of 1.20≤x≤2.10, and y falls within a range of 0.95≤y≤1.60) crystal.